Method for detecting and decoding a signal in a MIMO communication system

ABSTRACT

A method for detecting and decoding a signal in a communication system based on Multiple-Input Multiple-Output (MIMO)-Orthogonal Frequency Division Multiplexing (OFDM). A signal is received through multiple receive antennas. A decision error occurring at a symbol decision time is considered and a symbol is detected from transmitted symbols. Original data transmitted from the detected symbol is recovered. The performance of a coded bit system can be significantly improved using a new equalization matrix G considering a decision error.

PRIORITY

This application claims priority under 35 U.S.C. § 119 to an applicationentitled “Method for Detecting and Decoding a Signal in a MIMOCommunication System” filed in the Korean Intellectual Property Officeon Mar. 22, 2005 and assigned Serial No. 2005-23795, the contents ofwhich are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to a wireless communicationsystem, and more particularly to a method for detecting and decoding asignal in a Multiple-Input Multiple-Output (MIMO) communication system.

2. Description of the Related Art

A Multiple-Input Multiple-Output (MIMO) communication system transmitsand receives data using multiple transmit antennas and multiple receiveantennas. A MIMO channel formed by Nt transmit antennas and Nr receiveantennas is divided into a plurality of independent spatial subchannels.Because the MIMO system employs multiple transmit/receive antennas, itoutperforms a Single-Input Single-Output (SISO) antenna system in termsof channel capacity. Conventionally, the MIMO system undergoes frequencyselective fading that causes Inter-Symbol Interference (ISI). The ISIcauses each symbol within a received signal to distort other successivesymbols. This distortion degrades the detection accuracy of a receivedsymbol, and it is an important noise factor affecting a system designedto operate in a high Signal-to-Noise Ratio (SNR) environment. To removethe ISI, a stage at the receiving end has to perform an equalizationprocess for a received signal. This equalization requires highprocessing complexity.

On the other hand, Vertical Bell Labs Layered Space-Time (V-BLAST)architecture, which is one of space division multiplexing schemes,offers an excellent tradeoff between performance and complexity. TheV-BLAST scheme uses both linear and non-linear detection techniques. Inother words, the V-BLAST scheme suppresses interference from a receivedsignal before detection and removes interference using a detectedsignal.

When an Orthogonal Frequency Division Multiplexing (OFDM) scheme isused, an equalization process for the received signal is possible at lowcomplexity. An OFDM system divides a system frequency band into aplurality of subchannels, modulates data of the subchannels, andtransmits the modulated data. The subchannels undergo differentfrequency-selective fading according to transmission paths betweentransmit and receive antennas. The ISI incurred due to this fadingphenomenon can be effectively removed by prefixing each OFDM symbol witha cyclic prefix. Therefore, when the OFDM scheme is applied to the MIMOsystem, the ISI is not considered for all practical purposes.

For this reason, it is expected that the MIMO-OFDM system based on adetection algorithm of the V-BLAST scheme will be selected as anext-generation mobile communication system. However, the conventionalV-BLAST scheme has a severe drawback. There is performance degradationdue to error propagation, which is inherent in a decision feedbackprocess. Various methods are being studied and proposed to overcome thisperformance degradation. However, these methods create new problems,such as increased processing complexity of a receiving stage. Thiscomplexity increases according to a modulation level and the number ofantennas. The currently proposed methods are based on an iterativeprocess between detection and decoding without significantly increasingthe overall processing complexity.

SUMMARY OF THE INVENTION

Accordingly, the present invention has been designed to solve the aboveand other problems occurring in the prior art. It is an object of thepresent invention to provide a method for detecting and decoding asignal that can improve the reliability of a received signal bydetecting the signal while considering a decision error in anequalization process for the received signal.

It is another object of the present invention to provide a method fordetecting and decoding a signal that can improve system performance byoptimizing a signal detection order for channel-by-channel layers.

It is yet another object of the present invention to provide a methodfor detecting and decoding a signal that can reduce complexity bysetting a signal detection order for one channel and applying the setsignal detection order to all channels.

In accordance with an aspect of the present invention, there is provideda method for detecting and decoding a signal in a communication systembased on MIMO-OFDM, including the steps of receiving a signal throughmultiple receive antennas; considering a decision error occurring at asymbol decision time and detecting a symbol from the received signal;and recovering original data transmitted from the detected symbol.

Preferably, the symbol is detected using a Minimum Mean Square Error(MMSE)-based equalization matrix. The equalization matrix is expressedby $\begin{matrix}{{Equation}\quad(1)\text{:}} & \quad \\{{G = \quad{H_{\quad i}^{*}\left( \quad{{H_{\quad i}\quad H_{\quad i}^{*}}\quad + \quad{\frac{1}{\quad\sigma_{\quad s}^{\quad 2}}\quad{\quad\hat{H}}_{i\quad - \quad 1}\quad Q_{\quad{\quad\hat{e}}_{i\quad - \quad 1}}\quad{\quad\hat{H}}_{i\quad - \quad 1}^{*}}\quad + \quad{\alpha\quad I_{\quad M}}} \right)^{- 1}}},} & (1)\end{matrix}$

where H_(i) is a channel matrix for an i-th signal, * is a complexconjugate, e is an estimation error, Q_(e) is a decision errorcovariance matrix of$e,{\alpha = \frac{\sigma_{n}^{2}}{\sigma_{s}^{2}}},$and I is an identity matrix.

The equalization matrix is designed such that a mean square value of theerror e=x_(i)−Gy_(i) is minimized.

The decision error covariance matrix Q_(e) is computed by Equation (2):$\begin{matrix}{{Q_{e} = \begin{bmatrix}{E\left\lbrack {{e_{1}}^{2}\left. {\hat{x}}_{1} \right\rbrack} \right.} & \cdots & {E\left\lbrack {e_{1}e_{i - 1}^{*}\left. {{\hat{x}}_{1},{\hat{x}}_{i - 1}} \right\rbrack} \right.} \\\vdots & ⋰ & \vdots \\{E\left\lbrack {e_{i - 1}e_{1}^{*}\left. {{\hat{x}}_{i - 1},{\hat{x}}_{1}} \right\rbrack} \right.} & \cdots & {E\left\lbrack {{e_{i - 1}}^{2}\left. {\hat{x}}_{i - 1} \right\rbrack} \right.}\end{bmatrix}},} & (2)\end{matrix}$

where E[e_(m)e_(n)*|{circumflex over (x)}_(m),{circumflex over (x)}_(n)]corresponding to a conditional expectation value indicates that errorse_(m) and e_(n) occur due to inaccurate decisions associated with{circumflex over (x)}_(m)≠x_(m) and {circumflex over (x)}_(n)≠x_(n).

Diagonal elements E[∥e_(m)∥²|{circumflex over (x)}_(m)] of the decisionerror covariance matrix Q_(e) indicate a mean square error value of thedetected symbol.

-   -   Diagonal elements E[∥e_(m)∥²|{circumflex over (x)}_(m)] of the        decision error covariance matrix Q_(e) are values considering        variance of a decision error e_(m) due to an inaccurate decision        associated with {circumflex over (x)}_(m).

A position of a component with a smallest value among diagonal elementsof the decision error covariance matrix Q_(e) determines a signaldetection order.

The step of detecting the symbol includes the steps of estimating apreviously transmitted symbol using decoded original data in a previousdecoding process; and removing a component of the estimated symbol fromthe received signal.

The step of detecting the symbol includes the step of setting adetection order for layers in which signals are received through anidentical subchannel.

The detection order for the layers is set in descending order from alayer with a highest channel capacity.

The channel capacity is computed by Equation (3): $\begin{matrix}{{C_{n} = {{\sum\limits_{k = 1}^{N_{e}}{C_{nk}\quad{for}\quad n}} = 1}},\ldots\quad,N,} & (3)\end{matrix}$

where C_(nk) is defined as channel capacity for an n-th layer in a k-thsubchannel, C_(nk) being computed by Equation (4):C _(nk)=log₂(1+SINR _(nk)).  (4)

The detection order is set in ascending order from a layer in which ametric M_(n) for the n-th layer is smallest.

The metric M_(n) is computed by Equation (5): $\begin{matrix}{{M_{n} = {{\prod\limits_{k = 1}^{N_{e}}\quad{\left\lbrack \left( {{\left( {\rho/N} \right)\quad{\overset{\_}{H}}_{k}^{*}H_{k}} + I_{N}} \right)^{- 1} \right\rbrack_{m}\quad{for}\quad n}} = 1}},\ldots\quad,N,} & (5)\end{matrix}$

where H is a channel matrix, ρ is a mean received power to noise ratioin each receive antenna, and I is an identity matrix.

The detection order among layers is determined only for one particularsubchannel, and the same order is applied to all subchannels.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and advantages of the present invention willbe more clearly understood from the following detailed description takenin conjunction with the accompanying drawings, in which:

FIG. 1 illustrates a structure of a transmitter of a coded layeredspace-time OFDM system to which a signal detection and decoding methodof the present invention is applied;

FIG. 2 illustrates a structure of a receiver of the coded layeredspace-time OFDM system to which the signal detection and decoding methodof the present invention is applied in accordance with a firstembodiment of the present invention;

FIG. 3 is a 16-Quadrature Amplitude Modulation (16QAM) constellationillustrating a conditional probability used in the signal detection anddecoding method of the present invention;

FIG. 4 illustrates a structure of a receiver of the coded layeredspace-time OFDM system to which the signal detection and decoding methodis applied in accordance with a second embodiment of the presentinvention;

FIG. 5 illustrates performance comparison results between the signaldetection and decoding method of the present invention and theconventional V-BLAST method when 16QAM is applied in terms of a frameerror; and

FIG. 6 illustrates performance comparison results between the signaldetection and decoding method of the present invention and theconventional V-BLAST method when 64QAM is applied in terms of a frameerror.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be described in detail herein below withreference to the accompanying drawings.

FIG. 1 illustrates a structure of a transmitter of a coded layeredspace-time OFDM system to which a signal detection and decoding methodof the present invention is applied.

In FIG. 1, the OFDM transmitter is provided with a firstSerial-to-Parallel (S/P) converter 110 for converting an input bitstream to a plurality of parallel signal streams and signal processingunits associated with the signal streams output from the first S/Pconverter 110. The signal processing units are configured by encoders121-1˜121-n for encoding the signal streams, interleavers 123-1˜123-nfor interleaving signals output from the encoders 121, bit/symbolmappers 125-1˜125-n for performing bit/symbol mapping processes forsignals output from the interleavers 123, second S/P converters127-1˜127-n for converting symbol streams output from the bit/symbolmappers 125 to a plurality of parallel symbol streams, and Inverse FastFourier Transform (IFFT) processors 129-1˜129-n for performing EFFTprocesses for the parallel symbol streams output from the second S/Pconverters 127 to transmit signals through NT transmit antennas, TX 1˜TXN.

FIG. 2 illustrates a structure of a receiver of the coded layeredspace-time OFDM system to which the signal detection and decoding methodof the present invention is applied in accordance with a firstembodiment of the present invention.

In FIG. 2, the OFDM receiver is provided with Fast Fourier Transform(FFT) processors 210-1˜210-m for performing FFT processes for signalsreceived through M_(R) receive antennas RX 1˜RX M, a signal detectionunit 220 for processing parallel signals output from the FFT processors210-1˜210-m and outputting parallel signal streams associated with theFFT processors 210-1˜210-m, and signal processing units for processingthe parallel signal streams output from the signal detection unit 220according to signals associated with the FFT processors 210-1˜210-m. Thesignal processing units are configured by Parallel-to-Serial (P/S)converters 231-1˜231-m for converting the parallel signals associatedwith the FFT processors 210-1˜210-m to serial symbol streams, demappers233-1˜233-m for demapping the symbol streams output from the P/Sconverters 231 and outputting signal streams, deinterleavers 235-1˜235-mfor deinterleaving the signal streams output from the demappers 233, anddecoders 237-1˜237-m for decoding signals output from the deinterleavers235 and outputting original data.

In the present invention, it is assumed that channel state information(CSI) is predetermined for the receiver. The present invention considersa baseband signal model based on a zero-mean complex value and adiscrete-time frequency selective fading MIMO-OFDM channel model.

When an N-dimensional complex transmission signal vector and anN-dimensional complex reception signal vector are defined by x_(k) andy_(k), a signal received through the k-th subcarrier is expressed byEquation (6): $\begin{matrix}{{y_{k} = {{{\overset{\_}{H}}_{k}x_{k}} + n_{k}}}{where}{{\overset{\_}{H}}_{k} = {\begin{bmatrix}h_{{1l},k} & \cdots & h_{{1N},k} \\\vdots & ⋰ & \vdots \\h_{{M\quad 1},k} & \cdots & h_{{MN},k}\end{bmatrix}\quad{and}}}{n_{k} = \begin{bmatrix}n_{1} \\\vdots \\n_{M,k}\end{bmatrix}}} & (6)\end{matrix}$

Assuming that total power of x_(k) for obtaining the maximum capacity isP and a transmitter does not know a channel state, transmission signalpower must be equally distributed between N transmit antennas accordingto variance σ_(S) ². A covariance matrix of x_(k) is defined by Equation(7): $\begin{matrix}{{{E\left\lbrack {x_{k}x_{k}^{\dagger}} \right\rbrack} = {{\sigma_{S}^{2}I_{N}} = {\frac{P}{N}I_{N}}}},} & (7)\end{matrix}$

where E[•] and (•)^(†) denote an expectation value and a complexconjugate transpose matrix, respectively, I_(N) is an identity matrix ofa size N the additional term of n_(k) has variance σ_(n) ², and iscomplex Gaussian noise of an independent and identical distribution.

A channel coefficient h_(ji,k) of {overscore (H)}_(k) denotes a pathgain from the i-th transmit antenna to the j-th receive antenna. Thepath gain is modeled as a sample of independent complex Gaussian randomparameters having the variance of 0.5 on a dimension-by-dimension basis.If antennas of each stage on a communication link are divided accordingto more than a half wavelength, independent paths are maintained.

A signal model of a layered space-time OFDM system considering errorpropagation is newly introduced into the present invention. Transmissionsymbols are defined by x_(n) representing a symbol transmitted from then-th antenna and x=[x₁x₂ . . . x_(N)]^(T) representing a vector signalwith (•)^(T) representing the transpose of a vector. For convenience,the decision order {{circumflex over (x)}₁ {circumflex over (x)}₂ . . .{circumflex over (x)}_(i−1)} is designated by an optimum detection orderof the V-BLAST scheme proposed by Foschini.

{circumflex over (x)}_(n) denotes a symbol detected for Layer n, andh_(n) denotes the n-th row of {overscore (H)}.x _(i) =[x _(i) x _(i+1) . . . x _(N)]^(T) , H _(i) =[h _(i) h _(i+1) .. . h _(N) ], {circumflex over (x)} _(i−1) =[{circumflex over (x)} ₁{circumflex over (x)} ₂ . . . {circumflex over (x)} _(i−1)]^(T), and Ĥ_(i−1) =[h ₁ h ₂ . . . h _(i−1)].In the conventional V-BLAST algorithm, a symbol vector {circumflex over(x)}_(i−1) pre-detected until the (i−1)-th step is removed from a vectorsignal received in the i-th step. As a result, a corrected receivedvector y_(i) can be expressed by Equation (8): $\begin{matrix}\begin{matrix}{y_{i} = {y - {{\hat{H}}_{i - 1}{\hat{x}}_{i - 1}}}} \\{= {{H_{i}x_{i}} + n}}\end{matrix} & (8)\end{matrix}$

In Equation (8), it is assumed that the previous decisions are correct(i.e., {circumflex over (x)}_(n)=x_(n) for n=1,2, . . . , i−1). Thissignal detection process regards undetected signals {x_(i), x_(i+2), . .. , x_(N)} as interference, and is performed using a linear nullingprocess as in a Minimum Mean Square Error (MMSE) scheme. Equation (8)requires the accuracy of the pre-detected vector symbol {circumflex over(x)}_(i−1). In a situation in which a decision error is present,Equation (8) is rewritten as Equation (9): $\begin{matrix}{\begin{matrix}{y_{i} = {{\sum\limits_{j = i}^{N}{h_{j}x_{j}}} + {\sum\limits_{j = 1}^{i - 1}{h_{j}\left( {x_{j} - {\hat{x}}_{j}} \right)}} + n}} \\{= {{H_{i}x_{i}} + {{\hat{H}}_{i - 1}{\hat{e}}_{i - 1}} + n}}\end{matrix},} & (9)\end{matrix}$

where ê_(i−1)=[e₁e₂ . . . e_(i−1)]^(T) and e_(n)=x_(n)−{circumflex over(x)}_(n).

Next, an MMSE algorithm based on a new signal model of Equation (9) willbe described.

The present invention uses a nulling matrix based on an MMSE criterionconsidering a decision error. In the MMSE criterion, an equalizationmatrix G is designed such that a mean-square value of an errore=x_(i)−Gy_(i) is minimized, and can be obtained using the well-knownorthogonality principle in mean-square estimation as expressed inEquation (10):E[ey _(i) ^(†) ]=E[(x _(i) −Gy _(i))y _(i) ^(†)]=0  (10)

The equalization matrix G satisfies Equation (11).E[(x _(i) −Gy _(i))y _(i) ^(†) ]=Q _(x) _(i) _(y) _(i) −GQ _(y) _(i)=0,  (11)

where a covariance matrix is defined by Q_(AB)=E[AB^(†)] andQ_(A)=E[AA^(†)]. $\alpha = \frac{\sigma_{n}^{2}}{\sigma_{s}^{2}}$and G can be expressed from Equation (9) and Equation (11) as Equation(12): $\begin{matrix}\begin{matrix}{G = {Q_{x_{i}y_{i}}Q_{y_{i}}^{- 1}}} \\{{= {H_{i}^{\dagger}\left( {{H_{i}H_{i}^{\dagger}} + {\frac{1}{\sigma_{S}^{2}}{\hat{H}}_{i - 1}Q_{{\hat{e}}_{i} - 1}{\hat{H}}_{i - 1}^{\dagger}} + {\alpha\quad I_{M}}} \right)}^{- 1}},}\end{matrix} & (12)\end{matrix}$

where Q_(x) _(i) =σ_(S) ²I_(N−i+1) and Q_(n)=σ_(X) ²I_(M).

Therefore, a decision error variance matrix Q_(ê) _(i−1) of thedimension (i−1) can be defined as Equation (13): $\begin{matrix}{{Q_{{\hat{e}}_{i - 1}} = \begin{bmatrix}{E\left\lbrack {e_{1}}^{2} \middle| {\hat{x}}_{1} \right\rbrack} & \cdots & {E\left\lbrack {\left. {e_{1}e_{i - 1}^{*}} \middle| {\hat{x}}_{1} \right.,{\hat{x}}_{i - 1}} \right\rbrack} \\\vdots & ⋰ & \vdots \\{E\left\lbrack {\left. {e_{i - 1}e_{1}^{*}} \middle| {\hat{x}}_{i - 1} \right.,{\hat{x}}_{1}} \right\rbrack} & \cdots & {E\left\lbrack {e_{i - 1}}^{2} \middle| {\hat{x}}_{i - 1} \right\rbrack}\end{bmatrix}},} & (13)\end{matrix}$

where * denotes the complex conjugate and a conditional expectationvalue E[e_(m)e_(n)*|{circumflex over (x)}_(m),{circumflex over (x)}_(n)]is used to indicate that errors e_(m) and e_(n) occur due to inaccuratedecisions associated with {circumflex over (x)}_(m)≠x_(m) and{circumflex over (x)}_(n)≠x_(n), respectively.

For example, diagonal elements E[e_(m)e_(N)*|{circumflex over(x)}_(m),{circumflex over (x)}_(n)] indicate the variance of thedecision error e_(m) due to the inaccurate decision associated with{circumflex over (x)}_(m). Because non-diagonal elementsE[e_(m)e_(n)*|{circumflex over (x)}_(m),{circumflex over (x)}_(n)] donot have a correlation between errors where m≠n,E[e_(m)e_(n)*|{circumflex over (x)}_(m),{circumflex over (x)}_(n)] isthe same as E[e_(m)|{circumflex over (x)}_(m)] E[e_(n)*|{circumflex over(x)}_(n)].

When it is assumed that previously detected signals are perfect anderror propagation does not occur, the equalization matrix G proposed inthe present invention is equal to the conventional MMSE matrix. In otherwords, Q_(ê) _(i−1) =0.

Next, a method for deciding an optimum detection order on the basis of anew equalization matrix G in accordance with the present invention willbe described.

A covariance matrix Q_(e) of an estimation error e=x_(i)−Gy_(i) can becomputed after the equalization matrix G is set. Using Equation (12),the covariance matrix Q_(e) is expressed by Equation (14):Q _(e) =Q _(x) _(i) −Q _(x) _(i) _(y) G ^(†) −GQ _(y) _(i) _(x) _(i) +GQ_(y) _(i) G ^(†=σ) _(S) ²(I _(N−i+1) =GH _(i))  (14)

Diagonal elements indicate mean-square error (MSE) values of detectedsymbols. Therefore, the successive detection order depends on a positionof the smallest diagonal element of Q_(e). This is equal to a positionof the largest diagonal element GH_(i) of Equation (14).

Next, the operation of a demapper applied for the signal detection anddecoding method of the present invention will be described.

It is well known that the use of a soft output demapper and a soft inputchannel decoder significantly improves system performance. First, anoptimum soft bit metric considering a detection error is computed afterseveral assumptions are made in a detected vector signal {circumflexover (x)}_(i−1).

The index t denotes the position on the main diagonal of the matrixQ_(e) where the MSE is minimized. In other words, {circumflex over(x)}_(l) is selected as a decision at the i-th step where i≦t≦N. g_(l)is defined as the row of the equalization matrix G associated with anequalizer for {circumflex over (x)}_(i). Applying this equalizer vectorinto Equation (4) yields Equation (15): $\begin{matrix}{{\begin{matrix}{{\overset{\sim}{z}}_{t} = {{g_{t}H_{i}x_{i}} + {g_{t}{\hat{H}}_{i - 1}{\hat{e}}_{i - 1}g_{t}n}}} \\{= {{g_{t}h_{t}x_{t}} + {\sum\limits_{\underset{j \neq t}{j = i}}^{N}{g_{j}h_{j}x_{j}}} + {g_{t}{\hat{H}}_{i - 1}{\hat{e}}_{i - 1}} + {g_{t}n}}} \\{= {{\beta\quad x_{t}} + w}}\end{matrix},{where}}{\beta = {g_{t}h_{t}}}{and}{w = {{\sum\limits_{\underset{j \neq t}{j = i}}^{N}{g_{j}h_{j}x_{j}}} + {g_{t}{\hat{H}}_{i - 1}{\hat{e}}_{i - 1}} + {g_{t}{n.}}}}} & (15)\end{matrix}$

For analytical conveniences, it is assumed that the terms of w follow acomplex Gaussian distribution. An error probability of an MMSE detectorcan be easily assessed under an assumption that output interference andnoise are Gaussian noise.

Since each term in w is independent of other terms, the variance of wcan be computed by Equation (16): $\begin{matrix}\begin{matrix}{\sigma_{w}^{2} = {{\sum\limits_{\underset{j \neq t}{j = i}}^{N}{{{g_{t}h_{j}}}^{2}{E\left\lbrack {x_{j}}^{2} \right\rbrack}}} + {\sum\limits_{j = 1}^{i - 1}{{{g_{t}h_{j}}}^{2}{E\left\lbrack {e_{j}}^{2} \middle| {\hat{x}}_{j} \right\rbrack}}} +}} \\{E\left\lbrack {g_{t}{nn}^{\dagger}g_{t}^{\dagger}} \right\rbrack} \\{= {{\sum\limits_{\underset{j \neq t}{j = i}}^{N}{{{g_{t}h_{j}}}^{2}\sigma_{s}^{2}}} + {\sum\limits_{j = 1}^{i - 1}{{{g_{t}h_{j}}}^{2}{E\left\lbrack {e_{j}}^{2} \middle| {\hat{x}}_{j} \right\rbrack}}} + {\sigma_{n}^{2}{g_{t}}^{2}}}}\end{matrix} & (16)\end{matrix}$

In Equation (16), the second term corresponds to the decision error upto the (i−1)-th step, and it affects system performance significantly.After a biased term is properly scaled, the input to the unbiaseddemapper can be written as Equation (17):{tilde over (x)} _(i) ={tilde over (z)} _(i) /β=x _(i) +v,  (17)

where v is complex noise with the variance σ_(v) ²=σ_(w) ²/∥β∥².

Next, the computation of a Log Likelihood Ratio (LLR) for soft bitinformation will be briefly described.

Let S and s be a set of constellation symbols and an element of the setS, respectively. Then the conditional probability density function (pdf)of {tilde over (x)}_(i) in Equation (17) is given by Equation (18):$\begin{matrix}{{p\text{(}{\overset{\sim}{x}}_{t}\left. {x_{t} = s} \right)} = {\frac{1}{\pi\quad\sigma_{v}^{2}}\exp\quad\left( {- \frac{{{{\overset{\sim}{x}}_{t} - s}}^{2}}{\sigma_{v}^{2}}} \right)}} & (18)\end{matrix}$

When the i-th bit of x_(i) is defined as b_(l) ^(i) and two mutuallyexclusive subsets are defined as S₀ ^(o)={s:b_(l) ^(i)=0} and S₁^(i)={s:b_(l) ^(i)=1} where i=1,2 . . . log₂ M_(c) and M_(c) is definedas the constellation magnitude |S|, a posteriori LLR of b_(l) ^(i) canbe defined as Equation (19): $\begin{matrix}\begin{matrix}{{{LLR}\left( b_{t}^{i} \right)}\overset{\Delta}{=}{\log\frac{P\left\lbrack {b_{t}^{i} = \left. 0 \middle| {\overset{\sim}{x}}_{t} \right.} \right\rbrack}{P\left\lbrack {b_{t}^{i} = \left. 1 \middle| {\overset{\sim}{x}}_{t} \right.} \right\rbrack}}} \\{= {\log\frac{\sum\limits_{s \in S_{0}^{i}}{P\left\lbrack {x_{t} = \left. s \middle| {\overset{\sim}{x}}_{t} \right.} \right\rbrack}}{\sum\limits_{s \in S_{1}^{i}}{P\left\lbrack {x_{t} = \left. s \middle| {\overset{\sim}{x}}_{t} \right.} \right\rbrack}}}}\end{matrix} & (19)\end{matrix}$

Equation (19) can be rewritten through slight manipulation as shown inEquation (20): $\begin{matrix}{{{LLR}\left( b_{t}^{i} \right)} = {\log\frac{\sum\limits_{s \in S_{0}^{i}}{\exp\left( {- \frac{{{{\overset{\sim}{x}}_{t} - s}}^{2}}{\sigma_{v}^{2}}} \right)}}{\sum\limits_{s \in S_{1}^{i}}{\exp\left( {- \frac{{{{\overset{\sim}{x}}_{t} - s}}^{2}}{\sigma_{v}^{2}}} \right)}}}} & (20)\end{matrix}$

In order to compute σ_(v) ², E[∥e_(j)∥²|{circumflex over (x)}_(j)] mustbe computed for j=1,2, . . . , i−1 in Equation (16) and these quantitiesare related to the probability of decision error at the j-th step.

Next, a method for computing the error probability will be described.

The error probability associated with a Maximum Likelihood (ML) demapperis invariant to any rotation of a signal constellation. This means thatthe error probability depends on only a relative distance between signalpoints within the signal constellation. Let us define P_(e) as the errorprobability between two neighboring QAM signal points. Also, the minimumdistance of the M_(c)−QAM constellation is given by Equation (21):$\begin{matrix}{d_{\min} = \sqrt{\frac{6\sigma_{S}^{2}}{M_{C} - 1}}} & (21)\end{matrix}$

The error probability P_(e) between two signals separated by minimumdistance d_(min) is computed by Equation (22): $\begin{matrix}{{P_{e} = {Q\left( \frac{d_{\min}}{2\quad\sigma} \right)}},} & (22)\end{matrix}$

where${Q(x)} = {\int_{x}^{\infty}{\frac{1}{\sqrt{2\quad\pi}}\exp\quad\left( {- \frac{u^{2}}{2}} \right)\quad{\mathbb{d}u}}}$and σ² corresponds to the noise variation in an in-phase or 4-quadraturephase direction. Plugging d_(min) into Equation (22) yields Equation(23): $\begin{matrix}\begin{matrix}{\quad{P_{\quad e}\quad = \quad{Q\left( \quad\sqrt{\quad\frac{6\quad\sigma_{\quad S}^{\quad 2}}{\left( \quad{M_{\quad C}\quad - \quad 1} \right)\quad 4\quad\sigma^{\quad 2}}} \right)}}} \\{\quad{= \quad{Q\left( \quad\sqrt{\quad\frac{3\quad\sigma_{\quad S}^{\quad 2}}{\left( \quad{M_{\quad C}\quad - \quad 1} \right)\quad\sigma_{v}^{2}}} \right)}}}\end{matrix} & (23)\end{matrix}$

where the fact that σ² is a half the noise variance σ_(v) ² for the QAMsymbols is utilized. An accurate approximate value of the Q function hasbeen found over the range of 0<x<∞ as Equation (24): $\begin{matrix}{{{Q(x)} \simeq {\frac{1}{\sqrt{2\quad\pi}}\frac{\exp\quad\left( {- \frac{x^{2}}{2}} \right)}{\left\lbrack {{\left( {1 - a} \right)x} + {a\sqrt{x^{2} + b}}} \right\rbrack}}},} & (24)\end{matrix}$

where a=0.344 and b=5.334.

This error function is used to estimate conditional expectation valuesE[e_(l)|{circumflex over (x)}_(l)] and E[∥e_(l)∥²|{circumflex over(x)}_(l)].

FIG. 3 is a 16-Quadrature Amplitude Modulation (16QAM) constellationused to illustrate a conditional probability calculation in the signaldetection and decoding method of the present invention.

In FIG. 3, 16 signal points are classified into three categories: cornerpoints (S_(C0), S_(C1), S_(C2), and S_(C3)), edge points (S_(E0),S_(E1), S_(E2), S_(E3), S_(Er), S_(E5), S_(E6), and S_(E7)), and innerpoints (S₁₀, S₁₁, S₁₂, and S₁₃).

A process for computing E[e_(l)|{circumflex over (x)}_(l)] andE[∥e_(l)∥²|{circumflex over (x)}_(l)] values using Equation (23) isdescribed with reference to a conditional probability mass functionP(s|{circumflex over (x)}_(l)). The conditional probability massfunction P(s|{circumflex over (x)}_(l)) depends on a hard decision value{circumflex over (x)}_(l). It is only required to consider the followingthree cases in order to cover all the possible outcomes of {circumflexover (x)}_(l):

When {circumflex over (x)}_(l) belongs to the set of corner points, theconditional probability P(s|{circumflex over (x)}_(l)) of erroneousdetection into each neighbor signal point is shown in Table 1. TABLE 1 SS_(C0) S_(E0), S_(E2) S_(I0) P(s|{circumflex over (x)}₁) (1 − Q)² Q − Q²Q²

When {circumflex over (x)}_(l) belongs to the set of edge points, theconditional probability P(s|{circumflex over (x)}_(l)) of erroneousdetection into each neighbor signal point is shown in Table 2. TABLE 2 SS_(E0) S_(C0), S_(E1) S_(E2), S_(I1) S_(I0) P(s|{circumflex over (x)}₁)(1 − Q)(1 − 2Q) Q − Q² Q² Q − 2Q²

When {circumflex over (x)}_(l) belongs to the set of inner points, theconditional probability P(s|{circumflex over (x)}_(l)) of erroneousdetection into each neighbor signal point is shown in Table 3. TABLE 3 SS_(I0) S_(C0), S_(E1), S_(E4), S_(I3) S_(E0), S_(E2), S_(I1), S_(I2)P(s|{circumflex over (x)}₁) (1 − 2Q)² Q² Q − 2Q²

Here,$Q = {{Q\left( \sqrt{\frac{3\quad\sigma_{\quad s}^{\quad 2}}{\left( \quad{M_{\quad c}\quad - \quad 1} \right)\quad\sigma_{v}^{2}}} \right)}.}$Note that Q² term is negligible. In that case, only the closestneighbors are included.

Assuming that transmitted signals are equally likely, the conditionalprobability P(s|{circumflex over (x)}_(l)) that s is transmitted whenthe detected signal is {circumflex over (x)}_(l) falls into one of 3categories described above.

When only an error between two adjacent constellation signal points isconsidered, the conditional expectation values E[e_(l)|{circumflex over(x)}_(l)] and E[∥e_(l)∥²|{circumflex over (x)}_(l)] are computed byEquation (25) and Equation (26), respectively: $\begin{matrix}{{{E\text{[}e_{t}\left. {\hat{x}}_{t} \right\rbrack} = {\sum\limits_{s \in N_{{\hat{x}}_{t}}}{\left( {s - {\hat{x}}_{t}} \right){P\left( s \right.}{\hat{x}}_{t}\text{)}}}}{and}} & (25) \\{{E\text{[}{e_{t}}^{2}\left. {\hat{x}}_{t} \right\rbrack} = {\sum\limits_{s \in N_{{\hat{x}}_{t}}}{\left( {s - {\hat{x}}_{t}} \right){P\left( s \right.}{\hat{x}}_{t}\text{)}}}} & (26)\end{matrix}$

where the set N_({circumflex over (x)}) _(l) consists of neighboringconstellation signal points surrounding the hard decision signal point{circumflex over (x)}_(l). When the E[e_(l)|{circumflex over (x)}_(l)]and E[∥e_(l)∥²|{circumflex over (x)}_(l)] values are computed, the noisevariance σ_(w) ² of Equation (16) can be obtained and the covariancematrix Q_(ê) _(i) for the (i+1)-th step can be obtained from Equation(13).

In the signal detection and decoding method as described above, thecomplexity increases due to a process for computing the equalizationmatrix G. In the present invention the complexity O(NM³) is lower thanO(N³)+O((N−1)³)+ . . . +O(2³) in the conventional method.

FIG. 4 illustrates a structure of a receiver of the coded layeredspace-time OFDM system to which the signal detection and decoding methodis applied in accordance with a second embodiment of the presentinvention.

In FIG. 4, an FFT processor (not illustrated), a signal detection unit431, a P/S converter 433, a demapper 435, a deinterleaver 437, and adecoder 439 in the receiver in accordance with the second embodiment ofthe present invention have the same structures as those in the receiverof the first embodiment. The receiver of the second embodiment furtherincludes a representative layer order decision unit 440 for deciding thelayer order for an identical subchannel in output signals of the FFTprocessors and outputting a signal to the signal detection unit 431 inthe decided order. The receiver of the second embodiment furtherincludes a second encoder 441 for encoding an output signal of thedecoder 439 through the same encoding scheme as that of an associatedtransmitter, a second interleaver 443 for interleaving an output signalof the second encoder 441, a bit/symbol mapper 445 for performing abit/symbol mapping process for the interleaved signal from the secondinterleaver 443, and a layer canceller 447 for removing a component ofan associated symbol when the next repeated signal is detected in thesignal detection unit 431 using symbol information generated by thebit/symbol mapper 445.

When an interference cancellation method is applied, the performance ofan overall system is affected by the order in which each layer isdetected. It is very efficient that interference is removed usingdecision feedback information estimated from a decoder's output signalof the previous step in flat fading channels. In other words, alldecision values for the detected layer are transferred to the decoderwhen one layer is detected, and an output of the decoder is againencoded and is used for interference cancellation in the next layer.

Accordingly, all decision values detected in one layer must betransferred to the decoder in every detection step.

In accordance with the second embodiment of the present invention, thereceiver decides the detection order for a total layer according to onecomputation during a total detection process before the interferencecancellation is performed and applies the same detection order to allsubchannels.

In accordance with the second embodiment of the present invention, adecision element for deciding the detection order uses a channelcapacity value.

C_(nk) denotes Shannon capacity associated with i-th subchannel in n-thlayer and it is computed by Equation (27):C _(nk)=log₂(1+SINR _(nk)),  (27)

where for an unbiased MMSE filtering, SINR_(nk) can be expressed asEquation (28): $\begin{matrix}{{{SINR}_{nk} = {\frac{\sigma_{s}^{2}}{\sigma_{{{MMSE} - {LE}},{nk}}^{2}} - 1}},} & (28)\end{matrix}$

where σ_(MMSE−LE.nk) ² is an MMSE for the n-th layer in the k-thsubchannel. When Equation (12) is replaced by Equation (14),σ_(MMSE−LE.nk) ² is expressed by Equation (29): $\begin{matrix}\begin{matrix}{\sigma_{{{MMSE} - {LE}},{nk}}^{2} = \left\lbrack {{\sigma_{s}^{2}I_{N}} - {\sigma_{s}^{2}{\overset{\_}{H}}_{m}}} \right\rbrack_{nn}} \\{= \left\lbrack {{\sigma_{s}^{2}I_{N}} - {\sigma_{s}^{2}{{\overset{\_}{H}}_{k}^{*}\left( {{{\overset{\_}{H}}_{k}{\overset{\_}{H}}_{k}^{*}} + {\alpha\quad I_{M}}} \right)}^{- 1}{\overset{\_}{H}}_{m}}} \right\rbrack}\end{matrix} & (29)\end{matrix}$

Here, [A]_(ij) is the (i, j) element of a matrix A. In this case, theterms associated with decision errors are set to 0 (i.e., Q_(ê) _(i−1)₌₀).

Using the ABC lemma for matrix conversion, i.e.,(A+BC)⁻¹=A⁻¹−A⁻¹B(CA⁻¹B+I)⁻¹CA⁻¹, Equation (29) can be rewritten asEquation (30):σ_(MMSE−LE.nk) ²=[σ_(n) ²({overscore (H)} _(m) *{overscore (H)}_(m)+α1_(N))⁻¹]_(m)  (30)

When Equation (28) and Equation (30) are inserted into Equation (27),the capacity C_(nk) is computed by Equation (31): $\begin{matrix}{C_{nk} = {- {\log_{2}\left( \left\lfloor \left( {{\left( {\rho/N} \right){\overset{\_}{H}}_{k}^{*}H_{k}} + I_{N}} \right)^{- 1} \right\rfloor_{m} \right)}}} & (31)\end{matrix}$

The aggregate capacity C_(n) of the n-th layer across all subchannels isgiven by Equation (32): $\begin{matrix}{{C_{n} = {{\sum\limits_{k = 1}^{N_{C}}{C_{nk}\quad{for}\quad n}} = 1}},\ldots\quad,N} & (32)\end{matrix}$

The detection order based on C_(n) can be selected.

An operation for selecting a layer in which C_(n) is maximized isidentical to the one for retrieving a layer in which a metric valueM_(n) in Equation (33) is minimized. $\begin{matrix}{{M_{n} = {{\prod\limits_{k = 1}^{N_{C}}\quad{\left\lbrack \left( {{\left( {\rho/N} \right){\overset{\_}{H}}_{k}^{*}H_{k}} + I_{N}} \right)^{- 1} \right\rbrack_{m}\quad{for}\quad n}} = 1}},\ldots\quad,N} & (33)\end{matrix}$

After the metrics M_(n) for all layers are computed, the detection orderamong layers is determined in an ascending order of M_(n). The detectionorder in the detection method in accordance with the present inventionmay be different in each step. Because a process for updating the orderin every step is not useful for the overall performance improvement, theupdate is not performed to reduce complexity when the representativedetection order is set in the first step. As illustrated in FIG. 4, therepresentative detection order decision is performed in therepresentative detection order decision unit 440 before the signaldetection unit 431. The layer order is set by a value of M_(n).Accordingly, the signal detection and decoding method provides astandard metric for deciding an optimum layer order in a frequencyselective MIMO-Orthogonal Frequency Division Multiple Access (OFDMA)environment.

FIGS. 5 and 6 are illustrating performance comparison results in termsof a frame error between the signal detection and decoding method of thepresent invention and the conventional V-BLAST method when 16QAM and64QAM are applied.

The number of transmit antennas and the number of receive antennas are4, a Convolutional Code (CC) at a code rate ½ is used, an OFDM schemedefined in the Institute of Electrical and Electronics Engineers (IEEE)802.11a standard based on a 64-length FFT is used, and an OFDM symbolinterval is 4 μs including a guard interval of 0.8 μs. In thesimulations, a 5-tap multipath channel with an exponentially decayingprofile is used. It is assumed that the frame length is one OFDM symbolinterval.

When 16QAM is applied as illustrated in FIG. 5, signal detection anddecoding methods of the present invention have gains of 5 dB and 7 dB ascompared with the conventional V-BLAST and demapping method at a FrameError Rate (FER) of 1%. When the signal detection and decoding methodsof the present invention are combined, a gain of 8 dB can be obtained.This performance gain can be extended for 64QAM as illustrated in FIG.6.

This improvement is obtained through soft bit metric generation anddecision error consideration in an equalization process of the signaldetection and decoding method in accordance with the present invention.

As described above, the signal detection and decoding method of thepresent invention can significantly improve system performance in acoded bit system using a new equalization matrix G considering adecision error.

It is expected that the signal detection and decoding method of thepresent invention can obtain various diversity gains associated withfrequency, space, and time diversities with a successiveinterference-canceling algorithm by introducing an optimum soft bitdemapper.

Because the signal detection and decoding method of the presentinvention can improve system performance by correcting an equalizationmatrix, it is expected that the maximum system performance can beimproved in a minimum increase in the complexity of a receiver.

While the present invention has been described with reference to thepreferred embodiments thereof, it will be understood by those skilled inthe art that various changes in form and detail may be made thereinwithout departing from the scope of the present invention as defined bythe following claims.

1. A method for detecting and decoding a signal in a communicationsystem based on Multiple-Input Multiple-Output (MIMO)-OrthogonalFrequency Division Multiplexing (OFDM), comprising the steps of:receiving a signal through multiple receive antennas; considering adecision error occurring at a symbol decision time and detecting asymbol from the received signal; and recovering original datatransmitted from the detected symbol.
 2. The method of claim 1, whereinthe symbol is detected using a Minimum Mean Square Error (MMSE)-basedequalization matrix.
 3. The method of claim 2, wherein the equalizationmatrix is expressed by:${G = {H_{i}^{*}\left( {{H_{i}H_{i}^{*}} + {\frac{1}{\sigma_{s}^{2}}{\hat{H}}_{i - 1}Q_{{\hat{e}}_{i - 1}}{\hat{H}}_{i - 1}^{*}} + {\alpha\quad I_{M}}} \right)}^{- 1}},$where H_(i) is a channel matrix for an i-th signal, * is a complexconjugate, e is an estimation error, Q_(e) is a decision errorcovariance matrix of e,${\alpha = \frac{\sigma_{n}^{2}}{\sigma_{s}^{2}}},$  and I is anidentity matrix.
 4. The method of claim 3, wherein the equalizationmatrix is designed such that a mean square value of the errore=x_(i)−Gy_(i) is minimized.
 5. The method of claim 3, wherein thedecision error covariance matrix Q_(e) is computed by:${Q_{e} = \begin{bmatrix}{E\text{[}{e_{1}}^{2}\left. {\hat{x}}_{1} \right\rbrack} & \cdots & {E\left\lbrack {e_{1}e_{i - 1}^{*}\left. {{\hat{x}}_{1},{\hat{x}}_{i - 1}} \right\rbrack} \right.} \\\vdots & ⋰ & \vdots \\{E\left\lbrack {e_{i - 1}e_{1}^{*}\left. {{\hat{x}}_{i - 1},{\hat{x}}_{1}} \right\rbrack} \right.} & \cdots & {E\text{[}{e_{i - 1}}^{2}\left. {\hat{x}}_{i - 1} \right\rbrack}\end{bmatrix}},$ where E[e_(m)e_(n)*|{circumflex over(x)}_(m),{circumflex over (x)}_(n)] corresponding to a conditionalexpectation value indicates that errors e_(m) and e_(n) occur due toinaccurate decisions associated with {circumflex over (x)}_(m)≠x_(m) and{circumflex over (x)}_(n)≠x_(n).
 6. The method of claim 5, whereindiagonal elements E[∥e_(m)∥²|{circumflex over (x)}_(m)] of the decisionerror covariance matrix Q_(e) indicate a mean square error value of thedetected symbol.
 7. The method of claim 5, wherein diagonal elementsE[∥e_(m)∥²|{circumflex over (x)}_(m)] of the decision error covariancematrix Q_(e) are values considering variance of a decision error ell,due to an inaccurate decision associated with {circumflex over (x)}_(m).8. The method of claim 5, wherein a position of a component with asmallest value among diagonal elements of the decision error covariancematrix Q_(c) determines a signal detection order.
 9. The method of claim5, wherein the step of detecting the symbol comprises: computing a loglikelihood ratio (LLR) value of a transmitted symbol x_(l) mapped to aposition t in which a mean square error (MSE) is minimized in thedecision error covariance matrix Q_(e); and setting a symbol mapped tothe LLR value.
 10. The method of claim 9, wherein the LLR value iscomputed by:${{{LLR}\left( b_{t}^{i} \right)} = {\log\frac{\sum\limits_{s \in s_{0}^{i}}{\exp\left( {- \frac{{{{\overset{\sim}{x}}_{t} - s}}^{2}}{\sigma_{v}^{2}}} \right)}}{\sum\limits_{s \in s_{1}^{i}}{\exp\left( {- \frac{{{{\overset{\sim}{x}}_{t} - s}}^{2}}{\sigma_{v}^{2}}} \right)}}}},$where b_(l) ^(i) is an i-th bit of the transmitted symbol x_(l), S is aset of received symbols, s is an element of the set S, S_(o) ^(i) is asubset of the set S in which a value of the i-th bit is 0, σ_(v) ²=σ_(w)²/∥⊕∥² is variance of remaining interference and noise v, andβ=g_(l)h_(l).
 11. The method of claim 10, wherein the remaininginterference and noise are computed by: $\begin{matrix}{\sigma_{w}^{2} = {{\sum\limits_{j = i}^{N}{{{g_{t}h_{j}}}^{2}{E\left\lbrack {x_{j}}^{2} \right\rbrack}}} + {\sum\limits_{j = 1}^{i - 1}{{{g_{t}h_{j}}}^{2}{E\left\lbrack {e_{j}}^{2} \middle| {\hat{x}}_{j} \right\rbrack}}} + {E\left\lbrack {g_{t}{nn}^{\dagger}g_{t}^{\dagger}} \right\rbrack}}} \\{{= {{\sum\limits_{\underset{j \neq t}{j = i}}^{N}{{{g_{t}h_{j}}}^{2}\sigma_{s}^{2}}} + {\sum\limits_{j = 1}^{i - 1}{{{g_{t}h_{j}}}^{2}{E\left\lbrack {e_{j}}^{2} \middle| {\hat{x}}_{j} \right\rbrack}}} + {\sigma_{n}^{2}{g_{t}}^{2}}}},}\end{matrix}$ where g_(l) is a column of the equalization matrix G. 12.The method of claim 1, wherein the step of detecting the symbolcomprises: setting a detection order for layers in which signals arereceived through an identical subchannel.
 13. The method of claim 12,wherein the detection order for the layers is set in descending orderfrom a layer with a highest channel capacity.
 14. The method of claim13, wherein the channel capacity is computed by:${C_{n} = {{\sum\limits_{k = 1}^{N_{c}}{C_{nk}\quad{for}\quad n}} = 1}},\ldots\quad,N,$where C_(nk) is defined as the channel capacity for an n-th layer in ak-th subchannel, C_(nk) being computed by C_(nk)=log₂(1+SINR_(nk)). 15.The method of claim 12, wherein the detection order is set in ascendingorder from a layer in which a metric M_(n) for the n-th layer issmallest.
 16. The method of claim 15, wherein the metric M_(n) iscomputed by:${M_{n} = {{\prod\limits_{k = 1}^{N_{c}}\quad{\left\lbrack \left( {{\left( {\rho/N} \right){\overset{\_}{H}}_{k}^{*}H_{k}} + I_{N}} \right)^{- 1} \right\rbrack_{in}\quad{for}\quad n}} = 1}},\ldots\quad,N,$where H is a channel matrix, ρ is a mean received power to noise ratioin each receive antenna, and I is an identity matrix.
 17. The method ofclaim 12, wherein the detection order is set only for one subchannel,the set detection order being equally applied to all subchannels.